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This university learning plan consists of a primer on discrete mathematics and its applications including a brief introduction to a few numerical analysis. My personal experience is the foundation of it. Wikipedia and other information sources, in English and Spanish, support it. Course educational materials — including video — by others, help to improve this plan.
reesueltas Please, be free for suggesting improvements see this section. This course is a primer on discrete mathematics and its applications including a very short introduction to a few numerical methods. Although in respect of scientific knowledge, it has no particular prerequisitessome prior background in maths mainly in algebra, calculus and probability and computing mainly in programming is welcomed but in no way presupposed. Regarding English languageit may be desirable that you are at a intermediate conversational level, e.
You might find out your English level taking this free online English test diofanticxs then you might improve your knowledge of the English languagefor instance, practising your English skills at your leveland many more things available on these pages by the British Council Prince of Asturias Award for Communication and Humanities For the discrete mathematics part of the course, students are encouraged to use the following book as a textbook:.
However, its eight edition is already available —https: As this book cover the vast majority of the material of the course — which, incidentally, corresponds to what is currently taught in hundreds of universities in the field of discrete mathematics —, students are encouraged to adopt and study it.
It is even a guidebook including suggested readings, Despite its encyclopaedic spirit, it is also a handbook including lists of key terms and results and review questions. In addition, it has a companion website: For instance, you can download a complete set of lecture slides: Ecuacionds these diofantidas websites include, among other material and resources, interactive demos, self assessments and extra examples.
On the other side, this book is accompanied by books describing solutions for each of the proposed exercisesfor instance, for the 5th and 7th US editions:. And also by the supplementary books exploring and discussing contents and solutions to the ‘computer projects’ and ‘computations and explorations’ sections, from the 7th US edition:.
Finally, you can download another supplement, one book about applications of discrete mathematicslast edition, paired with Rosen’s book 6th edition, in any case for you to study it once you finish the course, except for the chapters that are of interest to it:. For the short numerical calculus part of the course, students are encouraged to use the following book as a textbook:.
At the UEX library, you have electronic access to the 6th edition, in Spanish: To keep track of the project you have joined to, please follow the recommendations on ecuacionee descriptive pageparticularly on ‘The basics’ resueltss. Very well then I contradict myself, I am large, I contain multitudes. Song of Myself in Leaves of Grass I encourage you to eecuaciones them, to contribute with everything you learn about the topics we deal with, to contrast with Wikipedia in other languages if you know them, to gather information from other texts, in short, to drink in good sources.
And write new articles in the English-language Wikipedia. Ultimately, contribute to improve this free encyclopedia as you study and learn.
Illustrative examples, cases, exercises, problems. Based on what we have worked with so resuelltas, both preparatory exams will replicate the final exam in level, content and format. They are not graded by the teacher and they are not included in the calculation of the final grade. It is assumed that every inhabitant is either a knight or a knave. Mind you, we will declare the variables precisely if we do not forget to do it.
It turns out that the program has not compiled. Therefore, we have forgotten to declare the variables.
Do not do it using truth tables. Lewis Carroll, Symbolic Logic: Elementary Macmillan,pg. So there are three possible solutions: Thus, the possible numbers are: How many of each device did they buy? Solve this question using the theory of:. From Wikipedia, the free encyclopedia. Read all of this web page carefully because it contains important information for you. Keep the link to it in safe custody, you may need to read this web page again.
All of that does not matter to me That is for those who do science, I just apply it. Obras Completas de Miguel de Unamuno, Vol. VIII Ensayospp.
It is important that you become aware that joining the university project ‘Discrete numerical mathematics’ is optional. Therefore, it is entirely up to you to do it.
But if you do it, remember, you are required to: Logic Sets, relations and functions Algebraic structures Cardinality and induction. Finite difference equations recurrence relations. Graphs Numerical calculus Complimentary knowledge pills Editathons. By way of example, some good sources on the web are: Enciclonet Divulgamat AznarEnrique R. Argumentation theory Axiology Critical thinking Logic in computer science Mathematical logic Metalogic Metamathematics Non-classical logic Philosophical logic Philosophy of logic Set theory.
Mathematical logic Boolean algebra Set theory. Logicians Rules of inference Paradoxes Diotanticas Logic symbols. Law of excluded middle Double negative elimination Law of noncontradiction Principle of explosion Monotonicity of entailment Idempotency of entailment Commutativity of conjunction De Morgan’s laws Principle of bivalence Propositional logic Predicate ecuacione.
Formal system Deductive system Axiomatic system Hilbert style systems Natural deduction Sequent calculus. Propositional calculus and Boolean logic.
Boolean functions Propositional calculus Propositional formula Logical connectives Truth tables Many-valued logic. First-order Quantifiers Predicate Second-order Monadic predicate calculus. Diofanticws Recursive set Recursively enumerable set Decision problem Church—Turing thesis Computable function Primitive recursive function.
Intuitionistic logic Constructive analysis Heyting arithmetic Intuitionistic type theory Constructive set theory. Degree of truth Fuzzy rule Fuzzy set Fuzzy finite element Fuzzy set operations. Structural rule Relevance logic Linear resueotas. Theseus’ ship List of Ship of Theseus examples Sorites. Petersburg Thrift Toil Tullock Value. Russell’s paradox Suslin’s problem Burali-Forti paradox. Algebraic number theory Analytic number theory Geometric number theory Ecuafiones number theory Transcendental number theory Combinatorial number theory Arithmetic geometry Arithmetic topology Arithmetic dynamics.
Numbers Natural numbers Prime numbers Rational numbers Irrational numbers Algebraic numbers Transcendental numbers p-adic numbers Arithmetic Modular arithmetic Arithmetic functions.
Quadratic forms Modular forms L-functions Diophantine equations Diophantine approximation Continued fractions. Divisibility-based sets of integers. Integer factorization Divisor Unitary divisor Divisor function Prime factor Fundamental theorem of arithmetic Arithmetic number. Untouchable Amicable Sociable Betrothed.
Classes of natural numbers. Centered triangular Centered square Centered pentagonal Centered hexagonal Centered heptagonal Centered octagonal Centered nonagonal Centered decagonal Star.
Wikipedia:School and university projects/Discrete and numerical mathematics/Learning plan
Centered tetrahedral Centered cube Centered octahedral Centered dodecahedral Centered icosahedral. Tetrahedral Octahedral Dodecahedral Icosahedral Stella octangula.
Square pyramidal Pentagonal pyramidal Hexagonal pyramidal Heptagonal pyramidal. Centered pentachoric Squared triangular. Carmichael number Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler—Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime Lucas pseudoprime Somer—Lucas pseudoprime Strong pseudoprime. Amicable Betrothed Deficient Semiperfect. Aronson’s sequence Ban Pancake number. Binary Euclidean Extended Euclidean Lehmer’s.
Eisenstein prime Gaussian prime.
– On-line Bookstore. Editorial URSS Publishers. Moscow: Mathematics.
Probable prime Industrial-grade prime Illegal prime Formula for primes Prime gap. Very important warning [ edit ].
The following exercises with solution are sample exam questions and answers for the contents of the course. You should be able to respond any of them in a maximum of 30 minutes. It is highly important that you keep in mind that when you sit an exam, both theoretical including proofs of theorems and practical questions about all topics worked out in class may be asked. The concreteness of the questions within the context of these examples implies in no case a course content cut.
Rigor when it comes to carrying out the solutions must be the central focus.
Show what you do and how you do it. Do not simplify your answers, write legibly and explain your work, showing all intermediate stepsseeking to ensure that your arguments are clear and logically diofantjcas. Label, or define, any variables and notation you choose to work with; also explain how you are solving each question as you go along, for example, stating clearly any theorem or result you use ; neatness, cleanliness and organization count.
You might like to see these exercises as seeds to help you in finding examples to illustrate your contributions to the project on Wikipedia.